Without going into the detail and the equations, you may find some help in this single point:
We'll look at the simple case of a single phase 208 to 240 transformer, made up of a single 208V to 32V transformer.
Primary winding AB and secondary winding CD. You make an autotransformer by connecting B to C. You can then think of this as one winding, A (BC) D.
You connect the incoming 208 to A and (BC) and take the output between A and D. If the full 30A load current flowed through A (BC) D, the transformer would have to be rated for at least 240V x 30A.
But if you look at the actual current flow, the 30A going to the load comes in at (BC) and passes though the larger guage winding only to get to D. The current through A (BC) is only the lower current needed to allow 30A to pass through (BC) D.
This means that the power rating of the transformer only needs to be 32V x 30A.